Chapter17:

RealOptionsObjectiveRealOptionsDeferralOptionBlack-ScholesFormulaRealOptions1Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallChapter17Contents17.1InvestinginRealOptions17.2DeferralOptions:TheCaseofUncertaintyandIrreversibility17.3ApplyingtheBlack-ScholesFormulatoValueRealOptions2Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallIntroductionWeshowhowtoapplyfinancialeconomictheorytostrategicdecisionmaking.Weshowhowoptiontheorymaybeappliedtoevaluatemanagement’sabilitytotimethestartofaninvestmentproject,toexpandit,ortoabandonit,afterithasbegun3Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall17.1InvestinginRealOptionsTodatewehaveignoredmanagement’sabilitytodelaythestartofaprojectexpandaprojectabandontheprojectFailuretotaketheseoptionsintoaccountwillresultinanunderstatedNPV4Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheMovieIndustry(Example)WewillexamineadecisioninthemovieindustryinordertounderstandtheimportanceofoptionsinevaluatingprojectsWeaddsomehypotheticalnumbers,andtokeepthecentralideasclearlyinfocus,theexamplewillthesimplestpossible5Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDerwynProductions:TimeA,RightsPurchaseDecisionDerwynProductions,isconsideringpurchasingtheexclusivemovierightsto“UnfinishedBusiness.”(Anunpublishedbook,authoredbyLouGrymshewwhohasseveralmovie‘hits’,andacoupleof‘bombs’)Cost$1MillionifpurchasedCost$0Millionifnotpurchased6Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDerwynProductions:TimeB,Book’sDebut(Event)CriticsandthepublicprovideinformationvaluableindeterminingtheultimatesuccessofthemovieManagementhasnoinfluenceoverthisnode7Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDerwynProductions:TimeC,ProductionDecisionContingency:Successfulbook(Prob=0.5) Makethemovie,NPVofmovie=$4millionDon’tmakethemovie,NPVmovie=$0millionContingency:Unsuccessfulbook(Prob=0.5)Makethemovie,NPVofmovie=-$4millionDon’tmakethemovie,NPVmovie=$0million8Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDerwynProductions:DecisionTree(yes,no)Buythemovierightstobook?(Cost$1Million)(Probability=0.5)MaketheMovie?(NPV-$4Million)(Probability=0.5)Makethemovie?(NPV$4Million)BookaSuccess?9Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDecisiontoAcquireRightsIfthedecisiontoundertaketheprojectismadeundertheassumptionofasingleup-frontdecisionthentheprojectmustalwaysberejectedBut…IfDerwynmakesthelogicalmanagerialdecisionateachstage,then(aslongasthecostofcapitalfortheprojectislessthan100%)theprojectshouldbeundertaken10Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallVolatilityandProjectEvaluationThereisacommonnotionthatriskininvestmentdecisionsissomethingthatneedstobepenalized:RiskycashflowsareoftendiscountedatahigherrateBut…wehavejustseenaninvestmentdecisioncontaininganoption-likefeature,andweknowthatoptionsalwaysbecomemorevaluablewithhighervolatility11Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall“UnfinishedBusiness”Thepublisheralsohasanotherbook,“RiskyBusiness,”andDerwynbelievesthatit’sidenticalto“UnfinishedBusiness”inalleconomicrespectsotherthanthepayoff,whichis(-$8million,8million)Runningthenumbersshows:themorevolatileprojectincreasesshareholders’wealthmorethanthelessvolatileone12Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallSummarySomeprojectsarenaturallyrichinvaluablemanagerialoptions(R&D),whileotherprojectshaveoptionsthatarerelativelyhardtofind,andthendiscovered,arenotparticularlyvaluable(fast-foodfranchisee)Sometimes,management’sabilitytorecognizetheoptionsinabusinesssituationisthekeythatdistinguishesawinningbusinessfromitslesssuccessfulsiblings13Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall17.2DeferralOption:TheCaseofUncertaintyandIrreversibilityInvestmentsinprojectscanbeundertakennoworpostponedPostponingordeferringaprojectallowsmanagerstoobtaininformationaboutfuturepayoffs14Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheDecisiontoInvestDecision:Buildafactorytoday,oneyearlater,ornotatallCosttobuild,I,zerosalvagevalue,zerooperatingcosts(zeromarginalcosts)Oneunitofoutputproducedperyear,currentpriceofoutputPo.Pricenextyearandeveryyearthereafter:P1=P2=P3=...=P∞

15Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDecisiontoInvest(continued)Futurepriceuncertain:itcangoupbyuwithaprobabilityofq;itcangodownbydwithaprobabilityof1-q.Valueofproject(assumeperpetualcashflows),NPVo(I,Po,q,u,d,r)whereristhediscountrateNPVo=-I+Po+Po[q(1+u)/r+(1-q)(1-d)/r]16Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDecisiontoInvest(Continued)

I=$1,600,Po=$200,u=$100,d=$100q=.5,1-q=.5.Expectedvalueofperpetualcashflowswhenpriceis$300:.5($300)/.10=$1500Expectedvalueofperpetualcashflowswhenpriceis$100:.5($100)/.10=$500ExpectedNPVo= ?$1600+$200+$1500+$500=$60017Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDecisiontoInvest(Continued)Att=1weknowwhatthepricewillbe,either$100or$300.IfP1=$100,NPV1=?$1600+$100+$100/.10=-$500andwerejecttheproject.IfP1=$300,NPV1=?$1600+$300+$300/.10=$1700andweaccepttheproject.18Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDecisiontoInvest(Continued)TheexpectedNPVoftheprojectatt=ois:[.5(1700)+.5(0)]/.10=$772.73Noteattime1ifP1=$100wedonotundertaketheprojectandNPV1=0Conclusion:Optiontodeferinvestmentisvaluable,NPVatt=oincreasesby$172.73=$772.73-$600.0019Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallNPVProfilesforCurrentandDeferredDecisions20Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallNPVSensitivitiestoInitialPriceParameter(P0)21Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallNPVSensitivitiestoInitialInvestmentCost(I)22Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallValueoftheDeferralOptionUsingtheBinominalOptionPricingModelConsiderthedeferraloptionasacalloptiononastreamoffactoryoutputoneperiodfromnowandthattheexercisepriceoftheoptionistheinvestmentcostofthefactory,soE=I.Valueofcallatmaturity:C1(P1)=P1+P1/r–IifP1+P1/r>I 0otherwise23Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDeferralOptionUsingBinomialOptionPricingModelCon’tValueofcontingentclaims:C1(100)=0,C1(300)=$1700Valueofhedgeratioh:h=[C1(300)-C1(100)]/($300-$100)=8.524Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDeferralOptionUsingBinomialOptionPricingModelCon’tCashflowsassociatedwithhedgedportfolio:CFo=CFo–8.5($200),CF1=8.5P1+(0.10)8.5(200)–C1(P1)Ifthepricefallsthepayoffis:8.5($100)+$170-0=$1020Ifthepricerisesthepayoffis:8.5($300)+$170-$1700=$102025Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDeferralOptionUsingBinomialOptionPricingModelCon’tNowfindCFo,theinitialoutlayneededtolockin$1020onperiodlater:CFo=-Co+8.5($200)=$1,020/1.10=$927.27Solveforthecurrentvalueofthedeferraloption:Co=8.5($200)-$927.27=$1700-$927.27=$772.73Conclusion:Donotexercisetheoptiontoinvesttoday,investoneyearlaterwhenpriceuncertaintyisresolved.

26Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall17.3ApplyingtheBlack-ScholesFormulatovalueRealOptionsThissectionshowshowtoapplytheBlack-Scholesoptionpricingformulaincapitalbudgetingbyusingtwoexamples27Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallRaider’sTakeoverofTargetusinganoptionSupposethatRaiderInc.isconsideringacquiringTargetInc.Assume:thatbothcompaniesare100%financedbyequitydividedinto1-millionsharesthatTargetisworth$100,000,000TargetoffersRaidertheoptiontopurchase100%ofTarget’ssharesoneyearfromnowRf=6%,costofoption$6million,sTarget=0.2028Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallRaider’sTakeoverofTargetUsingOptions:ComputationObservethattheTargetsFutureisequaltotheoption’sstrike,sothesimplifiedBSequationmaybeusedTheNPVoftheinvestmentistherefore$(8-6)millions=$2millions(doit)Thepremiumdistributedtotheshareholders29Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallImplicitOptions:ElectroUtilityElectroUtilityhastheopportunitytoinvestinaprojecttobuildapower-generatingplantPhase1:invest$6millionnowforthebuildingPhase2:purchaseequipmentcosting$106millioninoneyear30Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallImplicitOptions:ElectroUtilitySupposethat,viewedfromtoday’sperspective,thevalueofthecompletedplantis$112thestandarddeviationofthecapitalreturnfromtheprojectis0.2031Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallImplicitOptions:Electr